"Tristan Milos Trump was born at 2:59 a.m. on Sunday October 2," the couple tells Us Weekly exclusively. "He weighed 8 lbs 4 oz and came a week early. Mom and baby are doing great. He looks forward to meeting you all!"

Adds proud grandfather Donald to Us: "I am delighted that Don and Vanessa have a beautiful new member of their growing family."

Tristan gets his middle name from his paternal great-grandfather, Milos, father to Ivana Trump.

The couple, who married in 2005, are already parents to daughter Kai, 4, and son Donald III, 2.

Little Tristan is the second grandchild this year for mogul Donald Trump Sr., 65: His daughter Ivanka Trump welcomed her first child, daughter Arabella Rose, in June. The dad is publisher hubby Jared Kushner.